If m∠ABC

Question

is 160°
, and m∠ABD
is 92°
, what is the angle measure of DBC
? ∠ABD
and ∠DBC
are adjacent angles inside ∠ABC
.(1 point)
Responses

80°
80 degrees

160°
160 degrees

92°
92 degrees

68°

Answer 1

To find the measure of angle \( \angle DBC \), we can use the fact that the sum of the angles around point B in \( \angle ABC \) must equal the measure of \( \angle ABC \).

Given:

• \( m\angle ABC = 160° \)
• \( m\angle ABD = 92° \)

Using the property that the sum of adjacent angles is equal to the angle they form: \[ m\angle ABC = m\angle ABD + m\angle DBC \]

Substituting the given values: \[ 160° = 92° + m\angle DBC \]

Now, we can isolate \( m\angle DBC \): \[ m\angle DBC = 160° - 92° \] \[ m\angle DBC = 68° \]

Therefore, the measure of \( \angle DBC \) is 68 degrees.